As a mom, controlling how much presence my kids have online is a daily concern — and challenge. When he was 8 years old, I didn’t want my son on Facebook, didn’t want him to have his own cell phone — the most popular age at which U.S. kids get one is 12 — and didn’t want him to have his own e-mail address. I realize it’s inevitable, but as the mom, I get to control when it happens. Two years later, he’s just as cut off from the digital world as he was. I simply can’t see how spending more time in a virtual world instead of exploring the real one around him will contribute positively to his childhood.

Apparently, I’m not the only parent who feels like that — although I’m not certain I’m willing to pay cash for my convictions as Paul Baier, a father in Boston, intends to do.

Baier and his 14-year-old daughter inked a deal that calls on her to abstain from Facebook from Feb. 4 to June 26. In return, he’ll pay her $50 if she can stay off through April 15 and $150 more if she makes it to the end of June. Nor is this a simple time-out: Dad, who describes himself as vice president of sustainability consulting and research at Groom Energy Solutions, plans to deactivate Rachel’s account.

In the contract, Baier’s daughter is delightfully vague in her description of how she’ll use her riches. The document posted on her father’s blog states: “I plan to use the money for the following purpose: stuff.”

What’s more, the impetus behind their daddy-daughter contract is the daughter, who apparently came up with the idea.

Reaction on Baier’s blog has been mixed. Some accuse him of poor parenting, others praise him and hope that other moms and dads will follow suit. One person, Alisha Burkett, wondered: “What’s stopping her from opening another account in a different name and still getting the money? Just curious …”

Good point. The contract makes no mention of what is supposed to happen come July.

But even if Baier’s daughter should be unable to resist the pull of the world’s largest social-networking site, the five-month hiatus is an opportunity to regroup.

“This dad took the bull by the horns and created a win-win here,” says Dr. Gwenn O’Keeffe, a pediatrician outside Boston who is the author of CyberSafe, about protecting kids online. “It gives her the break from Facebook that she’s asking for, so that when she goes back on, it’s a time to sit down with her and ask, What was it that made you need a break?”

O’Keeffe, who has two girls ages 15 and 18, says her daughters thought that Facebook was overwhelming when they were younger. “They found it big and chaotic and a lot of their friends did too,” says O’Keeffe. “If it was just too much for her, then it’s an opportunity for the father to help her manage it better. There has got to be a reason that she felt she needs to go off it.”

Was she being cyberbullied? Did she feel excluded? Kids need guidance navigating social media — when should they comment and when should they ignore? What’s the appropriate tone to use? And in what situations should they involve an adult? In fact, says O’Keeffe, it’s a good idea for all parents to regularly check in with their Facebooking progeny.

“I have a niece who just doesn’t have an account because she’s seen so many kids addicted that has chosen to stay off it,” says O’Keeffe. Like Baier’s daughter, she’s not unique in making that move: 61% of Facebookers say they’ve taken a break of at least a few weeks from the site and more than a quarter say they plan to waste, er, spend less time on the site this year, according to data from the Pew Research Center.